I think where you are off with the logic is where I was initially also. Think of it as a weird calculator that when you enter an integer it outputs something else.

Look at it like this:

The operation on a integer M is either 3M or 1/2M...
So,

The operation on 9 outputs 3*9 = 27

and the operation on 6 outputs 6/2 = 3

The operations outputs multiplied equals 27*3 = 81

It asks which is equivalent which means,

which of these operations on the given integer equals 81?

The operation on 27 outputs 27*3 = 81.

HTH

For all positive integers m, [m] = 3m when m is odd and [m]=1/2m when m is even.Which of the following is equivalent to [9] x [6]

[9] is odd = 3x9 = 27
[6] is even = 1/2 x 6 = 3
[9] x [6] = 27 x 3
Above can be written as 3 x 27 = [27] is odd

Answer is D.

hmmmm interesting ... I also fell into the trap, and chose answer A (81). I guess the lesson-learned here is to read the question carefully !
It is asking which of the answer options is "EQUIVALENT" to [9] x [6].